Hello
Each armee korps have his own BA (with RBA for reserve and LBA for Landwher during war )
here is his 1914 list with Home district (during war we found KBA: Kriegs BA for war BA and BIA for Beckleidung Instandsetzung Amt for repair BA)
BA I :I Armeekorps Köenigsberg
BA II; II AK Stettin
BA III: III AK Berlin
BA IV IV AK Magdeburg
BA V: V AK Posen
BA VI: VI AK Breslau
BA VII / VII AK Münster
BA VIII : VIII AK Coblenz
BA IX: IX AK Altona
BA X : X AK Hannover (with Hannoversches, Brunswick and Oldenburg Regiment )
BA XI : XI AK Cassel
BA XII: First Sächsisches Armeekorps Dresden
BA XIII: Württembergisches AK Stuttgart
BA XIV: XIV AK Badisches
BA XV: XV AK Strassburg (Elsäss)
BA XVI : XVI AK Metz (Lothringen)
BA XVII: XVII AK Danzig
BA XIX: Second Sächsisches AK Leipzig
Armee korps without their own BA but with RBA (reserve)
XVIII AK Frankfurt a Main (with Hessisches regiments) depending of BA VII (IR 87 and 88)and BAVIII (for other)
XX AK Allenstein depending of BAI (IR 146, 147, 150 and 151) and
BA XVII (IR 18, 50, 148 and 152)
XXI AK Saarbrücken depending BA VIII (IR 70 and 174) and BA XV (for other)
Bavarians have their own BA ( three Armeekorps in München, Würburg and Nürnberg)
some are particulars like
BAG garde BA
BAO Ostasien (for China expeditionary armee korps)
KA for Kolonial Amt
To complete here is one interesting link
http://www.pickelhauben.net/articles/DepotMarks.htm
Regards